Question

(a) click on \take sample\ to see the results from your random sample of 35 suffolk sheep.

take sample

number of sheep
sample mean
sample standard deviation
population standard deviation
35
5.52
1.78
2.15

enter the values of the sample size, the point estimate for the population mean, the population standard deviation, and the critical value you need for your 99% confidence interval. (choose the correct critical value from the table of critical values provided.) then you are done, select \compute\.

sample size:
standard error:

point estimate:
margin of error:

population standard deviation:
99% confidence interval:

critical value:

compute

z_{0.005}=2.576
z_{0.010}=2.326
z_{0.025}=1.960
z_{0.050}=1.645
z_{0.100}=1.282

(b) based on your sample, graph the 99% confidence interval for the population mean of the birth weights for all suffolk sheep.

• enter the lower and upper limits on the graph to show your confidence interval.
• for the point (•), enter the publications claim of 4.29 kg.

99% confidence interval:
0.00
10.00
5.00
0.00
2.00
4.00
6.00
8.00
10.00

(c) does the 99% confidence interval you constructed contradict the publications claim? choose the best answer from the choices below.

• no, the confidence interval does not contradict the claim. the publications claim of 4.29 kg is inside the 99% confidence interval.
• no, the confidence interval does not contradict the claim. the publications claim of 4.29 kg is outside the 99% confidence interval.
• yes, the confidence interval contradicts the claim. the publications claim of 4.29 kg is inside the 99% confidence interval.
• yes, the confidence interval contradicts the claim. the publications claim of 4.29 kg is outside the 99% confidence interval.

Explanation:

Step1: Identify key values

Sample size $n=35$, point estimate $\bar{x}=5.52$, population standard deviation $\sigma=2.15$, critical value for 99% confidence $z_{0.005}=2.576$.

Step2: Calculate standard error

Standard error $SE=\frac{\sigma}{\sqrt{n}}=\frac{2.15}{\sqrt{35}}\approx0.364$.

Step3: Calculate margin of error

Margin of error $ME=z_{0.005}\times SE=2.576\times0.364\approx0.938$.

Step4: Compute confidence interval

Lower limit: $\bar{x}-ME=5.52-0.938\approx4.582$
Upper limit: $\bar{x}+ME=5.52+0.938\approx6.458$

Step5: Check claim against interval

Publication's claim is 4.29 kg, which is outside the interval (4.582, 6.458).

Answer:

(a) Sample size: 35, Point estimate: 5.52, Population standard deviation: 2.15, Critical value: 2.576
(b) Lower limit: ~4.58, Upper limit: ~6.46
(c) Yes, the confidence interval contradicts the claim. The publication's claim of 4.29 kg is outside the 99% confidence interval.